This is really strange. The writer used "check" instead of "cheque," so I would assume that they're talking about an American thing - but from a very short google search (http://www.investopedia.com/terms/c/crossedcheck.asp) it looks like crossed checks aren't really used in the US. (I know I've never heard of one. That link has some more information.) I would assume that "ready-crossed check" is one where the the crossing is pre-printed on the face of the check - but that's just a wild guess. As for your other question, "present" more or less means "give," but more officially/formally. I give you a gift at your party; the CEO of a company presents a charity with a gift at a formal gala. Banking still has some of this formalness/officialness around it. So, "presenting [your check] to the bank" means "handing the check to the person working at the bank."

Present, as a verb, means to show or give. So "presents it at a bank" means that the check is being shown at a bank. I had to look up "crossed check," because it's part of financial vocabulary that most people don't use. It appears to be a check that is marked with 2 parallel lines that indicates a given check can only be deposited into a bank account and not redeemed immediately for cash. So, a "ready-crossed" check, would be a check that originally has this "crossed" marking. I hope I've been able to help you. Good luck in your reading. Let me know if anything else is unclear.

"present" means "give" or "show" Ex: "Present your ticket at the front desk and you will be assigned a seat in the auditorium." A crossed check is a term I've never heard before, but it means that there are special intructions about how the check will be dealt with. Usually when you give a check to the person at the counter in a bank, you yourself can choose what you want done with the money it represents. You can ask for cash or have the money deposited into any bank account you wish. It seems with a crossed check can't be cashed (meaning the money in the form of paper and coin can not be given to the person who is presenting the check) but instead must immediately be put into a specified bank account.

"Present" has a few meanings, but you can see the verb definitions here: http://www.thefreedictionary.com/present (Look at Present², definition 2a.) This wikipedia page explains what a crossed check(/cheque) means. https://en.wikipedia.org/wiki/Crossing_of_cheques